A large variety of stationary and dynamic patterns are the results of the competition between nonlinear diffusion and aggregation effects,including the well
We study a general class of parabolic-parabolic Keller-Segel chemotaxis systems with/without growth source in a smooth bounded domain in higher dimensional
In this talk,we investigate the asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three d
We study positive steady states of a chemotaxis system with singular sensitivity in 1-D.Using the chemotactic coefficient as a bifurcation parameter,with an
We concerns with the existence and stability properties of nonconstant positive steady states in one dimensional space for the S-K-T model.By Lyapunov-Schmi
Amyloid diseases(which include Alzheimer's,Huntington's,Parkinson's etc)involve the aggregation of misfolded proteins.Elucidating the intrinsic mechanisms o
We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local al
Traditional models of yield stress fluids postulate a critical stress where a change from solid to fluid behavior occurs.Many yield stress fluids,however,ex
The polymerization of proteins is involved in numerous neurodegenerative diseases as prion or Alzheimer diseases.The growth-fragmentation PDE provides a rel
We develop a novel Bayesian level set approach for geometric inverse problems that arise in PDE-constrained applications.Our work consists of a rigorous app